Properties

Label 87.32
Level $87$
Weight $0$
Character 87.1
Symmetry even
\(R\) 2.658313
Fricke sign $+1$

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(2.65831358477065964200121898758 \pm 10 \cdot 10^{-8}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.39397716 \pm 4.6 \cdot 10^{-6} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.94317233 \pm 4.9 \cdot 10^{-6} \) \(a_{5}= -1.51624413 \pm 4.1 \cdot 10^{-6} \) \(a_{6}= -0.80481309 \pm 4.6 \cdot 10^{-6} \)
\(a_{7}= +1.29262177 \pm 3.9 \cdot 10^{-6} \) \(a_{8}= +0.07921648 \pm 4.7 \cdot 10^{-6} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +2.11360969 \pm 5.1 \cdot 10^{-6} \) \(a_{11}= +0.05178231 \pm 3.8 \cdot 10^{-6} \) \(a_{12}= +0.54454080 \pm 4.9 \cdot 10^{-6} \)
\(a_{13}= -0.60480649 \pm 3.5 \cdot 10^{-6} \) \(a_{14}= -1.80188523 \pm 5.0 \cdot 10^{-6} \) \(a_{15}= -0.87540396 \pm 4.2 \cdot 10^{-6} \)
\(a_{16}= -1.05359829 \pm 4.3 \cdot 10^{-6} \) \(a_{17}= +0.02575229 \pm 3.8 \cdot 10^{-6} \) \(a_{18}= -0.46465905 \pm 4.6 \cdot 10^{-6} \)
\(a_{19}= +1.98167765 \pm 3.9 \cdot 10^{-6} \) \(a_{20}= -1.43007951 \pm 5.1 \cdot 10^{-6} \) \(a_{21}= +0.74629553 \pm 3.9 \cdot 10^{-6} \)
\(a_{22}= -0.07218336 \pm 4.7 \cdot 10^{-6} \) \(a_{23}= -0.57115388 \pm 3.7 \cdot 10^{-6} \) \(a_{24}= +0.04573565 \pm 4.7 \cdot 10^{-6} \)
\(a_{25}= +1.29899627 \pm 4.2 \cdot 10^{-6} \) \(a_{26}= +0.84308644 \pm 4.7 \cdot 10^{-6} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +1.21916508 \pm 5.2 \cdot 10^{-6} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +1.22029312 \pm 8.8 \cdot 10^{-6} \)
\(a_{31}= +0.91574517 \pm 3.9 \cdot 10^{-6} \) \(a_{32}= +1.38947547 \pm 4.6 \cdot 10^{-6} \) \(a_{33}= +0.02989653 \pm 3.8 \cdot 10^{-6} \)
\(a_{34}= -0.03589810 \pm 5.0 \cdot 10^{-6} \) \(a_{35}= -1.95993017 \pm 4.1 \cdot 10^{-6} \) \(a_{36}= +0.31439078 \pm 4.9 \cdot 10^{-6} \)
\(a_{37}= +1.69804867 \pm 4.0 \cdot 10^{-6} \) \(a_{38}= -2.76241339 \pm 4.4 \cdot 10^{-6} \) \(a_{39}= -0.34918519 \pm 3.5 \cdot 10^{-6} \)
\(a_{40}= -0.12011152 \pm 4.8 \cdot 10^{-6} \) \(a_{41}= +0.72778207 \pm 3.6 \cdot 10^{-6} \) \(a_{42}= -1.04031892 \pm 8.5 \cdot 10^{-6} \)
\(a_{43}= -0.75239056 \pm 3.7 \cdot 10^{-6} \) \(a_{44}= +0.04883964 \pm 5.4 \cdot 10^{-6} \) \(a_{45}= -0.50541471 \pm 4.2 \cdot 10^{-6} \)
\(a_{46}= +0.79617547 \pm 4.6 \cdot 10^{-6} \) \(a_{47}= +0.50172887 \pm 3.8 \cdot 10^{-6} \) \(a_{48}= -0.60829525 \pm 4.3 \cdot 10^{-6} \)
\(a_{49}= +0.67087104 \pm 4.1 \cdot 10^{-6} \) \(a_{50}= -1.81077113 \pm 5.2 \cdot 10^{-6} \) \(a_{51}= +0.01486809 \pm 3.9 \cdot 10^{-6} \)
\(a_{52}= -0.57043675 \pm 4.8 \cdot 10^{-6} \) \(a_{53}= +1.86153888 \pm 3.6 \cdot 10^{-6} \) \(a_{54}= -0.26827103 \pm 4.6 \cdot 10^{-6} \)
\(a_{55}= -0.07851463 \pm 4.3 \cdot 10^{-6} \) \(a_{56}= +0.10239694 \pm 5.2 \cdot 10^{-6} \) \(a_{57}= +1.14412213 \pm 3.9 \cdot 10^{-6} \)
\(a_{58}= -0.25885506 \pm 4.6 \cdot 10^{-6} \) \(a_{59}= -0.81787540 \pm 3.7 \cdot 10^{-6} \) \(a_{60}= -0.82565679 \pm 9.1 \cdot 10^{-6} \)

Displaying $a_n$ with $n$ up to: 60 180 1000